Tag: reading graphs describing different situations

Questions Related to reading graphs describing different situations

Which of the following is true about the three lines
$L _{1}: x - 3y + 7 = 0 , L _{2} : 2x + y - 3 = 0$ and $L _{3} : 7x +\dfrac{7y}{2}-\dfrac{21}{2}=0$

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. Lines form a triangle

  2. Lines are concurrent

  3. Lines can not bound any region

  4. None of these

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Correct Option: C
Explanation:

Given equations of lines as
$L _{1}: x - 3y + 7 = 0 $
Slope of $L _{1}=\displaystyle \frac{1}{3}$
$ L _{2} : 2x + y - 3 = 0$ 
Slope of $L _{2}=-2$
$L _{3} : 7x +\dfrac{7y}{2}-\dfrac{21}{2}=0$
Slope of $L _{3}=-2$
$\Rightarrow L _{2}$ and $L _{3}$ are parallel
Hence, lines cannot bound any region.

The number of circles that touch all the straight
lines $x+y - 4 = 0, x - y+2 = 0$ and $y = 2$ is

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. 1

  2. 2

  3. 3

  4. 4

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Correct Option: D
Explanation:

The given lines form a triangle.
The number of circles are $4$, i.e. incircle and three ex-circles of the triangle. 

The points (4,0), (0,4), (-4,0), and (0, -4) form

maths sequences, functions and graphs reading graphs describing different situations using equations to plot lines basics of a straight line

  1. a rectangle

  2. a square

  3. a trapezium

  4. none of these

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Correct Option: B
Explanation:

From the diagram the points form a square

Find the equation of the straight line passing through the point $ (6,2)  $ and having slope $ -3 .  $

maths sequences, functions and graphs reading graphs describing different situations using equations to plot lines basics of a straight line

  1. $x-3y-10=0$

  2. $3x+y-20=0$

  3. $x+2y-40=0$

  4. $3x-y-10=0$

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Correct Option: B
Explanation:

Equation of any line is $y=mx+c$


here $m$ is slope of line 


so we have $m=-3$

$y=-3x+c$

Also this line passes through $(6, 2)$

$2=-18+c\Rightarrow c=20$

so equation of line will be $y+3x=20$

or $3x+y-20=0$.


A line passing through (2, 2) is perpendicular to the line $3x+y=3$. Its y intercept is _____________.

maths sequences, functions and graphs reading graphs describing different situations using equations to plot lines basics of a straight line

  1. $\dfrac { 1 }{ 3 } $

  2. $\dfrac { 2 }{ 3 } $

  3. 1

  4. $\dfrac { 4 }{ 3 } $

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Correct Option: A